Millian Efficiency with Endogenous Fertility

Abstract

Should governments implement policies that affect fertility decisions on efficiency grounds? What is the correct notion of efficiency to use? To address these issues, this paper develops an extension of the notion of Pareto efficiency, referred to as "Millian efficiency", to evaluate symmetric allocations in an overlapping generations setting with endogenous fertility. This extension is based on preferences of those agents who are actually alive, and exclusively allows for welfare comparisons of symmetric allocations. First, we provide necessary and sufficient conditions to determine whether an allocation is Millian efficient or not, and we show that the sufficient conditions for dynamic efficiency offered by Cass (1972) and Balasko and Shell (1980) cannot be directly applied when fertility decisions are endogenous. Second, we characterize Millian efficient allocations as the equilibria of a decentralized price mechanism, and we present a sufficient condition for dynamic efficiency that uses the sequence of prices associated to such decentralized equilibria. Finally, we analyse how intergenerational policies should be designed to restore efficiency and achieve net welfare gains in two different settings in which markets yield inefficient allocations: dynamic inefficiencies and financial market incompleteness regarding human capital. In the former, a pay-as-you-go social security system eliminates dynamic inefficiencies, provided pensions are explicitly linked with fertility decisions. In the latter, a specific link between social security and public education becomes a necessary condition for Millian efficiency. Copyright © 2009 The Review of Economic Studies Limited.

Property rights and efficiency in OLG models with endogenous fertility

“…Thus, there is no unique "optimal tax," but an entire range of large enough FDPAYG taxes that implement the same A−efficient allocation. Note that this result is different from Eckstein and Wolpin (1985), Abio, Mahieu, and Patxot (2004), Lang (2005) and Conde-Ruiz, Giménez, and Pérez-Nievas (2010), who all find a unique optimal fertility dependent tax level in related contexts but without altruism. 29 This result speaks to the current policy debate that blames low fertility rates for the insolvency of the standard PAYG systems around the western world.…”

“…An alternative policya fertility dependent PAYG system-on the other hand, can be used to implement an A−efficient allocation. Interestingly, we find that the same allocation can also be im- Samuelson (1958), Cass (1972), Balasko and Shell (1980) Eckstein and Wolpin (1985), Abio, Mahieu, and Patxot (2004), Lang (2005), Wigniolle (2007, 2009), Conde-Ruiz, Giménez, and Pérez-Nievas (2010) with altruism Barro (1974), Burbidge (1983) Razin and Ben-Zion (1975), Pazner and Razin (1980), This Paper plemented through birth subsidies financed by government debt and taxes. 11 This provides a potential rationale for currently observed government policies that subsidize children.…”

Egalitarianism under population change: Age structure does matter

“…The determination of the optimum relies on the following trade-off: on one hand, the utility function depends explicitly on population growth rate; on the other, population growth has the standard linear dilution effect on physical capital accumulation. Palivos and Yip proved that in such a framework the Benthamite criterion leads to a smaller population size and a higher growth rate of the economy provided the intertemporal elasticity of substitution is lower than one (consistently with 2 Another excellent reference is Conde-Ruiz et al (2010). 3 We could have fixed the terminology referring more to the role of γ in intertemporal discounting to show better the distance with respect to dynastic models.…”

Simple Analysis of Dynamic Efficiency in Endogenous Fertility

“…Golosov et al [1] and CondeRuiz et al [2] analyze the efficiency of the overlapped generation model with endogenous fertility. Although these literatures investigate the efficiency condition, they do not distinguish the difference between the condition of dynamic efficiency with endogenous fertility and without it.…”